2022/01/09 by Daichi Komori, Komori, Daichi
Mathematics · #32A38 #32A45 #32C38 #35A27 #58J15 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32A38 #msc:32A45 #msc:32C38 #msc:35A27 #msc:58J15
paper · pdf · doi:10.48550/arxiv.2201.02931
arxiv created 2022/01/09 · openalex publication_date 2022/01/09 · arxiv updated 2022/01/11 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
In this paper we construct the sheaf morphism from the sheaf of pseudodifferential operators to its symbol class. Since the map is hard to construct directly, we realize it with two original ideas as follows. First, to calculate cohomologies we use the theory of Čech-Dolbeault cohomology introduced by Honda, Izawa and Suwa. Secondly we construct a new symbol class, which is called the symbols of C^∞-type. These ideas enable us to construct the sheaf morphism, which is actually an isomorphism of sheaves.